GAUSSIAN RANDOM POLYGONS ARE GLOBALLY KNOTTED
GAUSSIAN RANDOM POLYGONS ARE GLOBALLY KNOTTED
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DOI：
10.1142/s0218216594000332
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发表时间：
1994-12
影响因子：
0.5
通讯作者：
D. Jungreis
中科院分区：
文献类型：
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作者：
D. Jungreis
高斯随机游走是一种随机游走，其中每一步都是一个坐标为高斯随机变量的向量。在三维空间中，如果一个n步的高斯随机游动开始和结束于原点，那么我们可以用直线段连接连续的点得到一个纽结。众所周知，如果n很大，那么结是非平凡的概率很高。我们给出了这个事实的新证明。我们的证明表明，此外，与高概率的结包含作为一个重要的循环在一个脂肪，打结，固体环面。因此，这个结是一个卫星结，任何微小的扰动都不能解开它。
A Gaussian random walk is a random walk in which each step is a vector whose coordinates are Gaussian random variables. In 3-space, if a Gaussian random walk of n steps begins and ends at the origin, then we can join successive points by straight line segments to get a knot. It is known that if n is large, then the knot is non-trivial with high probability. We give a new proof of this fact. Our proof shows in addition that with high probability the knot is contained as an essential loop in a fat, knotted, solid torus. Therefore the knot is a satellite knot and cannot be unknotted by any small perturbation.